Estimation of the impulse response of a system on the basis of binary observations

ABSTRACT

A method of identifying an electronic or electromechanical system includes: applying at least one noise signal (u) as input to the system, applying an output signal of the system to a one-bit analog digital converter, acquiring a signal at the output of the converter, carrying out an estimation of the output of the system with aid of performing an estimation (ĥ) of the impulse response of the system. The estimation (ĥ) of the impulse response includes: iterative calculation of a plurality of nh elements (J 0 , . . . , J i, . . . ,  J nh−1 ) of a given criterion (J), each element including, respectively: at least one term of correlation between the signal at the output of the converter and the noise signal.

TECHNICAL FIELD

The invention relates to the identification of systems, in particularfor electronic devices such as filters, for example, orelectromechanical devices, e.g. in MEMS form.

The invention relates to a device and a method carrying out anestimation of the output of a system by estimating its impulse responsein discrete time.

BACKGROUND OF THE INVENTION

In the traditional system identification means, quantificationoperations can be carried out. These operations are generally modeled byadding white noise b to a signal y that is quantified:y _(quantified) =y+b

This noise is all the weaker as the number of bits on which thequantification is done is higher. Thus, to identify a system using atraditional identification method, it is preferable to have an analogdigital converter (ADC) with a high resolution.

In that case, with a small number of measurements, it is possible to befreed from the quantification noise.

In the case where an ADC with low precision is used, a significantnumber of measuring points may be necessary.

One very widespread traditional identification method is the so-calledmethod “of least squares.” This method consists of making aparameterized model θ_(idéal) of the transfer function of the system andminimizing the square deviation between the measured values andestimated values output from the model Ĥ_(θ), the system's input e alsobeing known:θ_(idéal) =arg min(∥Ĥ _(θ)(e)−y _(quantifie)∥²)

In the case where the quantification noise is low enough, the quantifiedsignal y_(quantifié) can be likened to the actual signal y. In thatcase, if the model Ĥ_(θ) is linear, the parameterized model θ_(idéal)can be expressed analytically. The input e of the system one wishes toidentify is generally white noise.

The method of least squares has the drawback, in particular, ofrequiring that a high-resolution ADC be integrated.

In another method, called “KLV” (Kessler Landau Voda) (FIG. 1) (blockreferenced 2), the transfer function H of a system placed in anon-linear feedback loop is identified, including an adjustablehysteresis comparator 3. This comparator makes it possible to cause thesystem 2 to oscillate. Information can be deduced on the system throughthe appearance of said oscillations. A one-bit ADC 4 is provided inoutput of the system. It is then possible to connect, using analyticalrelationships, the amplitude and the frequency of the oscillationsarising in the system to the frequency response value of the system.Each hysteresis value has a corresponding point on the frequencyresponse curve.

Such a method has several drawbacks. First, the validity of theanalytical relationships used is based on an approximation calledapproximation of the first harmonic of the comparator. Moreover, such amethod requires a precise measurement of the amplitude and phase of theoscillations, the amplitude measurement requiring a high resolution ADC.

Another method, called “OBT” (Oscillation-Based Test), close to the KLVmethod, consists of inserting the system one wishes to identify andhaving a transfer function H, in a non-linear loop including acomparator 6. The return gain (block referenced 7) is adjusted toobserve oscillations preferably having as sinusoidal a shape aspossible. In this way, it is possible to deduce, using the firstharmonic hypothesis, the parameters of the transfer function H usinganalytical relationships, as for the KLV method.

This method also has the drawback of requiring a precise measurement ofthe amplitude of the oscillations at the input of the comparator, i.e. ahigh-resolution ADC 5 (FIG. 2).

An identification method called the “LCM”(Limit Cycle Measurement)method makes it possible to precisely determine the natural frequencyand damping of a second order system using two frequency measurements(FIGS. 3A and 3B).

A first measurement is done by placing the system to be identified withtransfer function H in a loop including a comparator 9 and adifferentiator 8 (FIG. 3A).

A second measurement is done by replacing, in said loop, thedifferentiator 8 with an integrator 10 (FIG. 3B).

It is thus possible to obtain a relationship between the frequency ofthe measured oscillations in output from the comparator 6 and the valueof the natural frequency and damping of the system to be identified.

This method is based on two digital measurements, the frequencymeasurement being done by counting the number of switches of thecomparator over a given duration. This method has several drawbacks.

It is only applicable to analog integrator or differentiator filters oron samples. Also, in the case of implementation using a digital circuit,it is necessary to have an Analog Digital Converter (ADC) with a goodresolution to inject the output of the integrator into the system.

In the “CLCM” (Complex Limit Cycle Measurement) method, the system to beidentified 12 is placed in a non-linear feedback loop including asampled comparator 13 having a sampling period Ts, a digitalprogrammable digital filter 14, and an ADC 15 (FIG. 4).

Depending on the value chosen for the coefficients of the digitalfilter, binary oscillations or “limit cycles” can be seen in output fromthe comparator 13. These limit cycles differ from those observed byimplementing the KLV method or LCM method in that they have a periodthat is a multiple of the sampling period Ts. The switching moments ofthe comparator 13 correspond to sampling moments. Thus, measuring alimit cycle corresponding to a set of coefficients of the programmablefilter 14 is completely digital.

This method in particular has the drawback of having to generate longlimit cycles to implement it.

The KLV and LCM methods make it possible to establish, at the cost of anapproximation, a relationship between the magnitudes measured andparameters one wishes to determine.

The KLV and OBT methods require a high-resolution ADC, while the LCMmethod requires an ADC with a good resolution. These methods yieldinsufficient results when the sampling frequency is high.

The CLCM method has a performance that is independent of the samplingfrequency, at the cost of heavier processing than that done with theother methods. Moreover, with such a method, good precision requiresthat long limit cycles be generated, which can be problematic.

The use of the aforementioned closed loop identification methods isparticularly problematic when the system to be identified is anelectromechanical device in the form of a MEMS. The risk is of not beingable to perform the identification at the right operating point, in asmuch as exciting a MEMS on one of its modes tends to very quicklyamplify non-linear phenomena. To offset this, it is possible to add anamplitude gain control (AGC) to the identification system, which mayrequire the use of a high-precision ADC.

The aforementioned identification methods have the drawback of requiringan analog-digital conversion with a significant resolution in output,which makes them more complex to implement and creates cost problems.

The problem arises of finding a new identification method that does nothave the aforementioned drawbacks.

BRIEF DESCRIPTION OF THE INVENTION

The present invention first concerns a method of identifying a systemcomprising the following steps:

-   -   applying at least one noise signal as input to the system,    -   applying an output signal y_(k) of said system to an analogue        digital converter, in particular a one-bit analogue digital        converter,    -   acquiring a signal s_(k) at the output of said converter,    -   carrying out an estimation ŷ_(k) of the output of said system        with the aid of means for performing an estimation ĥ of the        impulse response of said system comprising:    -   the iterative calculation of a plurality of nh elements J₀, . .        . , J_(i, . . . ,) J_(nh−1) (nh being an integer) of a given        criterion J each including: at least one term of correlation        between said signal at the output of said converter and said        input signal.

The output signal s_(k) is a binary data signal.

The method according to the invention makes it possible to perform anidentification without having to use a high-resolution ADC.

The input signal can be a noise signal.

The system is a device or a group of devices that can be described by atransfer function.

The system can be an electronic device, e.g. a filter, or a sigma-deltaconverter, or a telecommunications transmission channel, or a DC/DCconverter.

According to another possibility, the system can be an electromechanicaldevice, in particular in the form of a MEMS.

The given criterion J is also called “cost function.”

The estimation of the impulse response can also comprise: theapplication to said calculated elements of the given criterion, of a“passage” function f, said passage function f being predetermined as afunction of said signal applied at the input of said system, and suchthat:

${f(J)} = {\sum\limits_{i = 0}^{{nh} - 1}{h_{i}{\hat{h}}_{i}}}$

with h_(i) an impulse response element h of said system and ĥ_(i) anelement of said impulse response estimation ĥ of said system among aplurality of nh impulse response elements.

The estimation of the impulse response can comprise the application tothe calculated elements of the given criterion of a passage function fpredetermined as a function of the noise signal applied at the input ofthe system, so as to obtain a plurality of elements ĥ₀, . . . , ĥ_(i), .. . , ĥ_(nh−1) of said impulse response estimation ĥ, said elements ofsaid estimation being such that:(ĥ ₀ , . . . ,ĥ _(i) , . . . ,ĥ _(nh−1))=(f(J ₀), . . . ,f(J_(i))_(, . . . ,) f(J _(nh−1))).

According to one possibility, the input signal is a Gaussian noisesignal.

In that case, the passage function follows a given relationshipdetermined as a function of this type of noise.

In the case where the input signal is a Gaussian noise signal, saidpassage function f can follow the relationship: f(J)=σ′sin((π/2)(2J−1)), with:

σ′²=σ_(b) ²+σ_(h) ² where σ_(b), represents the ambient noise of thesystem to be identified modeled as an additive Gaussian white noise atthe output of the system and

$\sigma_{h}^{2} = {\sum\limits_{l = 0}^{\infty}h_{l}^{2}}$is the quadratic sum of the different elements of the impulse response.

According to another possibility, the input signal can be a white noisesignal.

In that case, the passage function follows a given relationshipdetermined as a function of that type of noise.

In the case where the input signal is a binary white noise signal, saidpassage function f can follow the relationship:f(J)=σ√{square root over (2)}((erf−1(1−2J))/√{square root over (1+2(erf⁻¹(1−2J))²)}

The estimation ĥ of the impulse response can comprise:

-   -   the transmission of the input signal u of the system through a        chain of blocks each forming a first order delay function or        each having z⁻¹ as a z transfer function,    -   the acquisition of values u_(k), . . . , u_(k−i), u_(k−nh−1) of        the noise signal at the output of said blocks respectively, said        elements J₀, . . . , J_(i, . . . ,) J_(nh−1) of said criterion J        being calculated with the aid of said values u_(k), . . .        u_(k−i), u_(k−nh−1) of the noise signal at the output of said        blocks, respectively.

The signal u is binary in the case of a binary white noise and onseveral levels in the case of Gaussian noise.

The values u_(k), . . . , u_(k−i), u_(k−nh−1) of the noise signal u aretaken at different moments k, k−1, . . . , k−i, k−nh−1.

The calculation of said plurality of nh elements J₀, . . . , J_(i), . .. , J_(nh−1) of said criterion J can comprise: applying the signal s_(k)at the output of said converter taken at a given moment k and a noisesignal u_(k−i), with (0≦i≦nh) at the output of said system, delayed itimes relative to said given moment, to a means forming an exclusive ORlogic gate.

Calculating said plurality of nh elements J₀, . . . , J_(i, . . . ,)J_(nh−1) of said given criterion J can comprise:

-   -   adding a term dependent on the result jk(n+1) of said        application of said exclusive OR function and a term of the cost        function calculated at the moment k−1 preceding said given        moment.

According to one possible embodiment of the method, the acquisition ofthe signal s_(k) at the output of said converter can be done for a givennumber N of samples, the calculation of the given criterion J beingdependent on at least one predetermined coefficient λ, with (λ)˜N, withN a given number of samples.

The method can comprise a modification of the value of said coefficientλ during said estimation of said impulse response ĥ.

Varying the coefficient λ can make it possible to modulate the precisionand speed of the estimation.

The estimation ŷ_(k) of the response also comprises: calculating aconvolution between the estimated impulse response ĥ and the noise inputsignal u.

A comparison of the output signal sk, and the estimation ŝk of thatoutput signal can be done over a given period to determine whether theestimation done is correct.

The modification of said coefficient λ can be done as a function of theevaluation of a second criterion Jt whereof the calculation is similarto that of the cost function J and that makes the comparison betweens_(k) and ŝ_(k).

Thus, the modification of said coefficient λ can be done as a functionof the evaluation of a second criterion Jt, the evaluation of saidsecond criterion Jt(n+1) at a given moment n+1 being done by iterativecalculation including at least one exclusive OR logic operation term XORbetween said output signal s_(k) of said converter and an estimationŝ_(k) of that signal, and a term depending on said second criterionJt(n) calculated at a moment n preceding the given moment.

The modification of the coefficient λ can be done as a function of theevaluation of said second criterion Jt and the result of the applicationof a predetermined second function ft to said second criterion Jt.

The second function ft can be an affine function, such that:ft(Jt)=λ=α*Jt+β(with α>0 and β>0) The coefficients α and β can for example be chosensuch that:

-   -   λ tends towards N when it tends towards 0    -   λ tends towards 2⁶ when it tends towards 1

The precision of the identification depends very little on the frequencyof the sampling and has a good robustness to the measuring noise.

At a given identification precision, the method according to theinvention requires fewer measuring points than the identificationmethods according to the prior art.

The method according to the invention is not based on an approximation,whether a “white noise” or “first harmonic” approximation, but rather onminimizing a criterion that, without approximation, depends on theone-bit quantification operation done by the analog-digital converter.

In the case where the system to be identified is a MEMS or an integratedelectronic circuit, the identification method has the followingadvantages relative to the methods according to the prior art:

-   -   it can be implemented using a sampled one-bit ADC, which allows        savings in terms of space and cost relative to methods requiring        the use of a high-resolution ADC,    -   it can operate in an open loop and does not disturb the system's        operating point,    -   the measurements are done close to the system to be identified,        a one-bit analog digital converter requiring few resources and        little surface area to be implemented, which minimizes the        measuring noise.

The invention also relates to a method of identifying an electronic orelectromechanical system, provided to carry out an identification methodas defined above.

The invention also relates to a device for identifying an electronic orelectromechanical system, comprising:

-   -   a means for generating a noise signal u, intended to generate a        noise signal at the input of said system,    -   a one-bit analog digital converter, to which an output signal        y_(k) of the system is intended to be applied,    -   a means for carrying out an estimation ŷ_(k) at the output of        the system, using an estimation ĥ of the impulse response of        said system comprising:    -   a first calculation means: to perform an iterative calculation        of a plurality of nh elements (with nh being an integer) J₀, . .        . , J_(i, . . . ,) J_(nh−1) of a given criterion J including at        least one correlation term between said signal output from said        converter and said noise signal.

An analog digital converter can be provided to generate an analogexcitation signal of the system.

The means for carrying out said estimation ŷ_(k) at the output of thesystem can also comprise: a second calculation means, provided to apply,to the calculated elements J₀, . . . , J_(i, . . . ,) J_(nh−1) of saidgiven criterion J, a passage function f predetermined as a function ofthe noise signal u_(k) transmitted at the input of said system, and suchthat:

${f(J)} = {\sum\limits_{i = 0}^{{nh} - 1}{h_{i}{\hat{h}}_{i}}}$

with hi an impulse response element h of said system and ĥi an elementof said impulse response estimation ĥ of said system.

The second calculation means can comprise one LUT or several LUTs.

The passage function f can be applied using a LUT, connected at theinput, to a multiplexer means, and at the output, to a demultiplexermeans.

According to one possible embodiment, the noise signal uk can be a whitenoise signal.

The means for generating said noise signal uk can comprise a LFSR randomsequence generator.

In the case where the input signal uk from the system is a white noisesignal, said passage function f can follow the relationship:f(J)=σ√{square root over (2)}((erf−1(1−2J))/√{square root over (1+2(erf⁻¹(1−2J))²)}

The impulse response estimation means can comprise: a chain of blocksrespectively forming a first order delay function or having z⁻¹as ztransfer function, said chain being intended to receive said inputsignal u_(k), and to transmit values u_(k), . . . u_(k−i), u_(k−nh−1)the delayed noise signal at the output of said blocks, respectively.

The first calculation means can comprise a means forming an exclusive ORlogic gate, to perform an exclusive OR logic operation between saidoutput signal sk of said comparator taken at a moment k and said noisesignal (uk−I, with 0≦i≦nh) delayed by i relative to said given moment.

The first calculation means can comprise an adding means, to add theresult of said logic operation to a term depending on an element of saidgiven criterion calculated previously.

The acquisition of the signal s_(k) at the output of said converter canbe done for a given number N of samples, the calculation of the givencriterion J by the first calculation means being dependent on at leastone predetermined coefficient λ, 1+λ being equal to said given number N.

The device can also comprise: a means for modifying the coefficientvalue λ during said estimation ĥ of said impulse response.

The first calculating means can comprise a means making it possible toapply said coefficient λ in the form of at least one shift registerand/or means for applying a ratio 1/(1+λ) in the form of at least oneshift register.

According to another possibility, the first calculating means cancomprise a means making it possible to apply a ratio (1/λ) in the formof at least one shift register.

The modification of the coefficient λ can be done as a function of theevaluation of a second criterion Jt. The calculating structure for thesecond criterion can be similar to that making it possible to calculatethe given criterion J.

The identification device can also comprise:

-   -   a means for evaluating said second criterion it including at        least one exclusive OR logic gate to perform an exclusive OR        logic operation between said output signal s_(k) from said        converter and an estimation ŝ_(k) of that signal,    -   an adding means, for adding the result of said logic operation        between said output signal s_(k) from said converter and an        estimation ŝ_(k) of that signal, to a term depending on an        element of said second criterion previously calculated.

The coefficient λ can be modified as a function of the evaluation ofsaid second criterion Jt, for example using the following relationship:λ=α*Jt+β(with α>0 and β>0)

-   -   With λ that tends towards N when Jt tends towards 0    -   λ that for example tends towards 2⁶ when it tends towards 1

The means for performing said estimation ŷ_(k) can comprise a means forconvolution calculation, provided to calculate a convolution between theestimated impulse response ĥ and the noise input signal.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be better understood upon reading thedescription of embodiments, provided purely for information andnon-limitingly, in reference to the appended drawings in which:

FIG. 1 provides an example of a device for carrying out a method ofidentifying a system according to the prior art, called KLV method.

FIG. 2 shows an example of a device for carrying out a method foridentifying a system of the prior art, called OBT method.

FIGS. 3A-3B illustrate another example of a method of identifying asystem according to the prior art, called LCM method.

FIG. 4 illustrates another example of a method of identifying a systemaccording to the prior art, called CLCM method.

FIG. 5 illustrates an example of a device for carrying out a method foridentifying a system according to the invention.

FIG. 6 illustrates an example of a LSFR noise generator integrated in adevice according to the invention.

FIG. 7 provides an example of a curve representative of an impulseresponse of an IIR filter.

FIGS. 8 a-8B provide examples of cost function calculation unitsintegrated into a device according to the invention and in particular astructure for estimating the output of a system to be identified withthe aid of an estimation of the impulse response of that system.

FIG. 9 provides an example of LUT in a device according to theinvention, for applying a passage function between a cost function andan estimated impulse response estimation element.

FIGS. 10A-10B provide examples of curves representative of predeterminedpassage functions in the cases of an input signal in the form of aGaussian noise injected into the system to be identified, and in thecase of an input signal in the form of a white noise, respectively.

FIG. 11 provides an example of a structure for calculating an impulseresponse estimation within a device according to the invention.

FIG. 12 provides an example of a convolution calculation structurebetween impulse response and an input signal of a system to beidentified, integrated into an identification device according to theinvention.

FIG. 13 illustrates an example of an impulse response estimationstructure and output of a system, within a device according to theinvention.

FIG. 14 provides an alternative of a cost function calculation unitintegrated in a device according to the invention, and in particular astructure for estimating the output of a system to be identified usingan estimation of the impulse response of that system.

FIG. 15 illustrates another example of an impulse response estimationstructure of a system, within a device according to the invention.

FIG. 16 provides another alternative of a cost function calculation unitintegrated into a device according to the invention, and in particular astructure for estimating the output of a system to be identified withthe aid of an estimation of the impulse response of that system.

FIG. 17 illustrates another example of an impulse response estimationstructure of a system within a device according to the invention.

FIG. 18 illustrates another example of an impulse response estimationstructure with one LUT of a system, within a device according to theinvention.

FIG. 19 illustrates another example of an estimation structure with onelevel, for estimating the impulse response of a system, within a deviceaccording to the invention.

FIG. 20 illustrates an example of a device for implementing a method foridentifying a system according to the invention, including a feedbackloop to modify the precision or speed of the estimation of an impulseresponse during that estimation.

FIG. 21 illustrates an example of a means for modulating a calculationcoefficient λ of a criterion J used to calculate an impulse responseestimation in a method according to the invention.

FIG. 22 illustrates an affine straight line of a relationship connectinga criterion Jt and a coefficient λ involved in the calculation of a costfunction.

FIG. 23 provides examples of curves representative of an impulseresponse estimation, obtained using a first device according to theinvention without a feedback loop, and using a second device accordingto the invention provided with a feedback loop, respectively.

FIGS. 24 and 25 illustrate an example of an identification deviceaccording to the invention in which the system to be identified is afilter, and an example of an impulse response curve of saididentification device, respectively.

FIG. 26 provides examples of impulse response estimation curvesdetermined using a simulation done using the matlab software andexperimentation done using a program written in VHDL and carried out ona FPGA target.

FIG. 27 illustrates an example of a system in the form of an activefilter, on which an identification method according to the invention hasbeen carried out.

FIGS. 28 and 29 provide examples of impulse response estimation curvesand gain of the filter of FIG. 27, obtained with the aid of anidentification device according to the invention.

FIG. 30 provides an example of an architecture for carrying out anidentification method according to the invention.

The different parts illustrated in the figures are not necessarily shownaccording to a uniform scale, to make the figures more legible.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

An example of a method according to the invention for identifying asystem and a device for carrying out such a method will now be given.

Such a method uses a processing called “BIMBO_inline” (“BasicIdentification Method Using Binary Observations,” “inline” meaning thatthe method uses identification with the aid of binary signals calledobservations and is done in real time) and can be implemented forexample using at least one digital signal processor (DSP), and/or atleast one microprocessor and/or at least one FPGA circuit and/or atleast one computer.

In FIG. 5, a block diagram equivalent to a device implementing such amethod is provided.

The identification comprises an estimation of the system's output, usingan estimation of the impulse response of that system.

The system to be identified is a system capable of being described by atransfer function.

The system to be identified can for example be an electronic device suchas a filter, a sigma delta converter, a DC/DC converter, or atelecommunications transmission channel.

The system to be identified can for example be an electromechanicaldevice, for example in the form of a MEMS.

First, a signal u is generated at the input of the system 100.

The signal u is preferably a discrete signal u_(k) with k representing amoment in discrete time. The signal u_(k) can be a spectrally richsignal such as a noise signal, in particular a Gaussian noise or a whitenoise.

In the case where the signal u is a Gaussian white noise, a digitalanalog converter can be used to generate the excitation of the observedsystem, the sign of the noise being exploited in the identificationmethod.

In the case of a binary white noise, a zero order hold can be used toexcite the observed system 100 and as input signal for the presentstructure.

The input signal u_(k) can be produced by a noise generator 110. A noisegenerator similar to those used in cryptography and which implements aLFSR (Linear Feedback Shift Register”) with a shift register can beused, for example. With such a generator, certain bits of a sequenceundergo operations or transformation before being reinserted in a loop.Such a generator is provided to produce pseudo-random sequences. Thegenerator can for example be of the 32^(nd) order LFSR typecorresponding to the following primitive polynomial:1+x+x³+x³⁰.

One example of a LFSR generator is given in FIG. 6. This generator isformed by a series of blocks 111, 112, 113, 114 having z transferfunctions equal to z⁻¹, z⁻², z⁻²⁸, z⁻¹, respectively. The generator alsocomprises a first summer 115, between the first block 111 and the secondblock 112, a second summer 116 between the second block 112 and thethird block 113, a third summer 117 between the third block 113 and thefourth block 114 being reinjected at the input of each of the summers115, 116, 117.

The method comprises several steps for acquiring input and outputsignals of the system 100 to be characterized or identified.

The response signal y_(k) is then injected in means forming a comparator120 at the output of which a sampled discrete output signal s_(k) istransmitted. The comparator 120 can be a one-bit ADC. This comparator120 can be provided to apply a signum S( ). Such a signum S( ) makes itpossible to perform the following processing:o=sign(x) and

0 then o=0o=sign(x) and x

0 then o=1

-   -   if:

The aim is to produce an estimation ŷ_(k) of the output of the system100, with the aid of a means 130 in the form of a processing block or aprocessing module intended to carry out the BIMBO_inline method.

The means 130 can form an approximate parametric model of the unknownsystem 100. The method makes it possible to make the approximate modelconverge as closely as possible with the observed actual system 100.

Estimation calculations ĥ of the impulse response of the actual systemare done by the means 130, the estimated impulse response having tocorrespond to that of the observed system, when the parametric modelconverges towards the actual system. The means 130 can for example beimplemented with the aid of a FPGA. According to other possibilities,the means 130 can be implemented with the aid of a digital signalprocessor (DSP), and/or a microprocessor, and/or a computer.

The calculations of the estimation ĥ are done from the input signal uand the output sign s of the comparator 120, these signals u and s beinginjected at the input of the means 130. These signals s and u are alsocalled “observations.” In the present case, the observations are in theform of binary signals.

The means 130 thus produces, as output, an estimation ŷ_(k) of theoutput of the system 100, which is injected into a second comparator140, for example in the form of a second one-bit ADC, to apply thesignum to that estimation. The signal Ŝ_(k)=S(ŷ_(k)), with S( ) beingthe signum, can then be compared to the signal s_(k) coming from thefirst comparator 120.

It may be considered that the estimation of ŷ_(k) done is satisfactorywhen s and ŝ are equal over a significant duration. “Significant”duration here refers to a period at least 1000 times the samplingperiod, for example corresponding to a number N of observation samplesin the vicinity of 8000 or 10000.

The method according to the invention makes it possible to obtain anestimation ŷ of the output of the system 100 observed with the aid of anestimation ĥ of its impulse response.

Throughout this description, “impulse response of a system” will referto the temporal output of that system when it is stimulated by animpulse. In the case of a discrete signal, the impulse response may beconsidered like the system's response to a Dirac type impulse. Theestimation of the system's impulse response 100 can be defined by a setof discrete elements ĥ_(i).

In FIG. 7, an example of a curve C₁ representative of an impulseresponse of a discrete IIR filter is given. In this figure, a number nhof elements of the impulse response is such that nh=50. The set of nhelements of an impulse response can be described via a set of points(h₀, h₁, h₂, . . . , H_(nh−1)).

The processing done by the means aims to obtain the followingrelationship:(h ₀ ,h ₁ ,h ₂,_(. . .) ,h _(nh))=({circumflex over (h)}₀ ,ĥ ₁ ,ĥ₂,_(. . .) ,ĥ _(nh))

With h_(i) being an element of an impulse response and ĥ_(i) being anelement of an estimated impulse response.

An error between the signal y and the estimation ŷ of that signal iscalled a prediction error. At a moment n, the prediction error E can bedefined as follows:ε(n)=y(n)−{circumflex over (y)}(n)

Through successive iterations, the model implemented by the means 130can be adjusted so as to correct the estimation ŷ_(k) produced andthereby maximize the similarities between the signal S_(k) and itsestimation S_(k)=S(ŷ_(k)).

This adjustment is done in particular using a calculation of a givencriterion J done by the means 130. This criterion J, which will also becalled “cost function,” depends on a set of observation acquired up to amoment n, with:J(n)=g(y(0)_(. . .) y(n),{circumflex over (y)}(0)_(. . .) {circumflexover (y)}(n),n)

In the present case, the output s( ) of the comparator 120 is exploitedin order to perform the calculation of said cost function. The costfunction can therefore also be written:J(n)=g(s(0)_(. . .) s(n),{circumflex over (s)}(0)_(. . .) {circumflexover (s)}(n),n)

To make it possible to evaluate an impulse response, a cost functionmeeting the following general formula can be implemented:

$J = {\frac{1}{4N}{\sum\limits_{N}\left( {s_{k} - {\hat{s}}_{k}} \right)^{2}}}$

The criterion J has a value between 0 and 1 and is minimal in the zoneof the parameter space of the parametric model that will be called the“acceptability zone” of the approximate parametric model.

Two different examples of calculations of the cost function J, includinga comparison term between the output signal s and the estimated outputsignal ŝ, will now be given.

According to a first possibility, one can have S(y_(k))ε[−1;1] with S( )being the signum. In that case, when:y _(k)>0=>S(y _(k))=1y _(k)<0=>S(y _(k))=−1The signals s and ŝ_(k) being coded on one bit.

We therefore have the following relationship:

$J = {{\frac{1}{4N}{\sum\limits_{N}\left( {s_{k} - {\hat{s}}_{k}} \right)^{2}}} = {\frac{1}{2} - {\frac{1}{2N}{\sum\limits_{N}{s_{k}{\hat{s}}_{k}}}}}}$

In this case we note:

${Csu} = {\frac{1}{N}{\sum\limits_{N}{s_{k}{\hat{s}}_{k}}}}$

With:

$J = {\frac{1}{2} - {\frac{1}{2}{Csu}}}$

A first example of a unit 200 (FIG. 8A) integrated in the means 130 canbe provided to carry out the iterative calculation of a cost functionelement Ji according to this first possibility. The means 130 with aunitary impulse response model, such that the calculation of Ji includesa correlation term between the signal s_(k) at the output of saidconverter and the noise signal:

$J_{i} = {\frac{1}{2} - {\frac{1}{2N}{\sum\limits_{N}{{s(k)}{u\left( {k - i} \right)}}}}}$

With Ji an element of the cost function, and N a number of calculationpoints or observations, of the processing done. This result J_(i) willthen be used to determine an i^(th) element ĥ_(i) of the estimation ofthe impulse response of the observed system. The result Ji, which is acost function element, corresponds to a correlation coefficient or acorrelation term between the output signal s and the input signal u ofthe system 100. The cost function element J_(i) is determined by aniterative calculation including a correlation term between the signal sand the signal u.

In this example, the cost function calculation element J_(i) unit 200comprises a means 202 forming a multiplier at the input of which anoutput signal s_(k) taken at a moment k and an input signal u_(k-i)delayed from i are transmitted.

The unit 200 also comprises a means 204 forming a summer at the outputof the multiplier 202, as well as a means 206 forming a first orderdiscrete delay filter, or a z transfer function block equal to z⁻¹ atthe output of the summer.

The output of the block 206 is reinjected at the input of the summer204, while a means 208 forming a divider by N (with N being the numberof samples or iterative calculation points on which the calculation isdone) at the output of the summer 204. A relooping is thus formed suchthat an element Ji(n+1) calculated at a given moment depends on anelements Ji(n) previously calculated.

At the output of the means 208, a correlation Csu is obtained between skand ŝk:

${Csu} = {\frac{1}{N}{\sum\limits_{N}{s_{k}{\hat{s}}_{k}}}}$

According to a second calculation possibility of the cost function, onecan have S(y_(k))ε[0;1]

In this case, when:y _(k)>0=>S(y _(k))=0y _(k)<0=>S(y _(k))=1

But the signals s and ŝ can be coded in binary and are capable ofadopting a ‘0’ state or a ‘1’ state.

The following calculation can be done:

$J = {{\frac{1}{N}{\sum\limits_{N}\left( {s_{k\;} - {\hat{s}}_{k}} \right)^{2}}} = {\frac{1}{N}{\sum\limits_{N}{{xor}\left( {s_{k},{\hat{s}}_{k}} \right)}}}}$

A second example of a unit 250 for calculating an element Ji of the costfunction J according to said second possibility is provided in FIG. 8B.This unit 250 can be provided to perform the following calculation:

$J_{i} = {\frac{1}{N}{\sum\limits_{N}^{\;}{{XOR}\left( {s_{k},u_{k - 1}} \right)}}}$

With Ji being an element of the cost function, and N a number ofsamples. The cost function element J_(i) is thus determined through aniterative calculation including a correlation term between the signal sand the noise signal u.

The unit 250 comprises a means 252 forming an exclusive OR logic gate(XOR) at the input of which the output signal s_(k) of the comparator120 at a moment k and the input signal u_(k−i) of the system 100 delayedby i are transmitted.

A means 254 forming a summer is provided at the output of the XOR gate,while a means 256 forming a first order delay filter or a z transferfunction block equal to z⁻¹ is placed at the output of the summer 254,the output of the block 254 being reinjected at the input of the summer254. The cost function element J_(i) thus depends on a cost functionelement calculated at a preceding moment. A means 258 intended toperform a division by N (with N being a number of samples) is alsoprovided at the output of the unit 250 and delivers the result J_(i)corresponding to a correlation coefficient between the signal s and thesignal u delayed by i sampling periods. This result J_(i) is then usedto estimate the i^(th) element ĥ_(i) of the impulse response of theobserved system.

δ is defined as a term to term product of elements of the impulseresponse (h₀, . . . , h_(i), . . . , h_(nh−1)) of the observed systemand estimations (ĥ₀, . . . , ĥ_(i, . . . ,) ĥ_(nh)) of impulse responseelements.

A “passage” function f connecting the cost function J to δ, with

$\delta = {{f(J)} = {\sum\limits_{i = 0}^{{nh} - 1}{h_{i}{\hat{h}}_{i}}}}$(hi being an impulse response element of the system and ĥi an impulseresponse estimation element of the system) is also implemented and usedby the means 130.

The passage function f is a function chosen so as to make it possible togo from the calculation of an element J_(i) of the cost function to avalue of an element ĥi of the estimation of the impulse response, suchthat f(J_(i))=ĥi. The passage function f is determined as a function ofthe input signal injected into the system 100.

The passage function f can be carried out using at least one storageunit called LUT (Look Up Table) and which makes an impulse responseestimation element ĥi value correspond to a cost function J element Jivalue. An example of a LUT 260 is given in FIG. 9. The LUT 260 ischaracterized in particular by its size and by a pitch Δ. The impulseresponse data is stored with a pitch Δ in the LUT, such that onlycertain image values of the passage function are accessible: valuesf(0), f(Δ), f(2*Δ), . . . . The LUT 260 thus yields output values eachcorresponding to a range of cost function J values.

According to one example, in the case where the input signal u is aGaussian noise, the passage function f from a cost function to animpulse response element can satisfy the following law:

$f = {\sigma^{\prime}{\sin\left( {\frac{\pi}{2}\left( {{2 \cdot J} - 1} \right)} \right)}}$

With J being the cost function and σ′²=σ_(b) ²+σ_(h) ² a where σ_(b),represents the ambient noise of the system to be identified modeled asan additive Gaussian white noise at the output of the system and

$\sigma_{h}^{2} = {\sum\limits_{i = 0}^{\infty}h_{l}^{2}}$the quadratic sum of the different elements of the impulse response.

By default one can choose σ′=1. It is then possible to identify theimpulse response of the system to the closest gain.

In FIG. 10A, an example of a curve C₁₀ representative of a passagefunction f between the criterion J and the impulse response is given ina case where the input signal u of the system 100 to be identified istransmitted in the form of a Gaussian noise.

According to another example, in the case where the input signal u is awhite noise, the passage function f from the cost function to theimpulse response can satisfy the following law:

${f({Csu})} = {{\sigma\sqrt{2}\frac{{erf}^{- 1}({Csu})}{\sqrt{1 + {2\left( {{erf}^{- 1}({Csu})} \right)^{2}}}}} = {\sum\limits_{i = 0}^{{nh} - 1}\;{h_{i}{\hat{h}}_{i}}}}$$J = {{\frac{1}{4N}{\sum\limits_{N}^{\;}{\left( {s_{k} - {\hat{s}}_{k}} \right)^{2}\mspace{14mu}{and}\mspace{14mu} J}}} = {\frac{1}{2} - {\frac{1}{2}{Csu}}}}$${Csu} = {\frac{1}{N}{\sum\limits_{N}^{\;}{s_{k}{\hat{s}}_{k}}}}$

We thus have:

${f(J)} = {\sigma\sqrt{2}\frac{{erf}^{- 1}\left( {1 - {2J}} \right)}{\sqrt{1 + {2\left( {{erf}^{- 1}\left( {1 - {2J}} \right)} \right)^{2}}}}}$

By default, σ can be chosen equal to 1.

In FIG. 10B, another example of a curve C₂₀ representative of a passagefunction f between the criterion J and the impulse response is given inthe case where the input signal of the system 100 to be identified is awhite noise.

In FIG. 11, an example of a module integrated with the means 130 andprovided with nh levels to perform a calculation of nh (nh being aninteger greater than 1) elements of an estimation ĥ of the impulseresponse of the system 100 is given.

This module first includes a plurality of nh−1 blocks forming a chain offirst order discrete delay filters: 240 ₁, . . . , 240 _(i), . . . , 240_(nh−1) each having a z transfer function equal to: z⁻¹.

At the input of the series of delay filters, the input signal u_(k) ofthe system 100 at a moment k is transmitted, delayed signals u_(k−1), .. . , u_(k−i), . . . , u_(nh−1), are obtained at the output of thefilters 240 ₁, . . . , 240 _(i), . . . , 240 _(nh−1), respectively.

A plurality of nh calculation units 250 ₀, . . . , 250 _(i), . . . , 250_(nh−1) of elements J₀, . . . , J_(i), . . . , J_(nh−1) of the costfunction J similar to the unit 250 described above relative to FIG. 9Bare also provided.

The cost function element calculation units 250 ₀, . . . , 250 _(i), . .. , 250 _(nh−1) each receive, as input, the output signal s_(k) from thecomparator 120 at a moment k and the signals u_(k), . . . , u_(k−1),u_(k−i), . . . , u_(nh−1), respectively, corresponding to delayed inputsignal values of the system 100.

The structure also includes a plurality of nh means 260 ₀, 260 ₁, . . ., 260 _(i), . . . , 260 _(nh−1) for applying the passage function f( ).The passage function can be that for which the law was provided above,in the case where the input u is a white noise signal. The means 260 ₀,260 ₁, . . . , 260 _(i), . . . , 260 _(nh−1) can assume the form of nhLUTs of the type described relative to FIG. 10, and receive, as input,cost function elements J₀, J₁, . . . , J_(i), . . . , J_(nh−1),respectively, and delivering, as output, impulse response estimationelements ĥ₀, ĥ_(l), . . . , ĥ_(i), . . . , ĥ_(nh−1).

From the impulse response estimation, it is possible to obtain anestimation ŷ of the output of the system 100. To that end, the followingcalculation is done by the means 130:

${\hat{y}(n)} = {\sum\limits_{k = 1}^{n}{{u(k)}{\hat{h}\left( {n - k} \right)}}}$

A convolution operation between the estimation ĥ of the impulse responseand the binary input u of the observed system 100 is done.

In FIG. 12, an example of a module 270 integrated with the means 130 andmaking it possible to perform said convolution operation is given. Thismodule includes a plurality of nh levels 270 ₀, 270 ₁, . . . , 270 _(i),. . . , 270 _(nh−1), respectively receiving, as input, input signalsu_(k), u_(k−1), . . . , u_(k−i), . . . , u_(k−nh+1) of the system atdifferent moments k, k−1, . . . , k−i, . . . , k−nh+1, and impulseresponse estimation elements ĥ₀, ĥ_(l), . . . , ĥ_(i), . . . , ĥ_(nh−1).

Each level of the module 270 includes multiplying means 271 of the twoinputs of the level as well as a means 273 for adding the output of themultiplying means 271 to an output from a preceding level, in otherwords, to add the result of said multiplication to the result of apreceding level. The module 270 for performing the convolution operationdelivers, as output, the estimation ŷ of the output y of the system 100.

In FIG. 13, an example of a complete structure for delivering anestimation ŷ is shown.

This structure 230 includes nh levels 231 ₀, 231 ₁, . . . , 231 _(i), .. . , 231 _(nh−1), the number of levels nh being able to be provided inparticular as a function of the complexity of the system 100 to beidentified. The non-zero elements of the impulse response of the systemare estimated. If the number of non-zero elements of the impulseresponse is noted n₀, n₀ and nh are such that nh>n₀.

This structure 230 includes a zero order filter or a z transfer functionblock: z⁻⁰, as well as a plurality of nh−1 blocks 240 ₁, . . . , 240_(nh−1), having as z transfer function: z⁻¹ or respectively forming afirst order delay filter, these blocks being arranged in a series or ina chain of blocks.

The structure 230 also includes nh units 250 ₀, . . . , 250 _(nh−1) forcost function evaluating elements J₀, . . . , J_(nh−1), units 260 ₀, . .. , 260 _(nh−1) LUTs to apply the passage function f and obtain impulseresponse estimation elements ĥ₀, . . . , ĥ_(nh−1), as well as nh units270 ₀, . . . , 270 _(i), . . . , 270 _(nh−1) to perform the convolutionoperation and produce the estimation ŷ.

In FIG. 14, another example of a cost function element calculation unit300 making it possible to perform the calculation of an element of acost function variation J′, different from the cost function Jpreviously described, is given. The cost function element is determinedby an iterative calculation including a correlation term between theoutput signal of the system and the input signal of the system.

The unit 300 comprises a means 302 forming an exclusive OR logic gate(XOR) at the input of which an output s_(k) of the comparator taken at amoment k is transmitted, and an inlet u_(k−i) of the system delayed by isamples.

The unit 300 comprises a means 304 forming a summer at the output of theXOR gate, a means 306 forming a first order delay filter at the outputof the summer 304 and the output of which is reinjected as input of themeans 303 to apply a coefficient λ, the output of the means 303 to applythe coefficient λ being transmitted as input of the summer 304. Theoutput of the summer is transmitted at the input of a means 308 forperforming a division by (1+λ). At the output of the means 308, anelement of said second cost function J′ is obtained.

The sum (1+λ) corresponds to a number N of samples or calculation pointsor observations.

In this example, the coefficient λ is also chosen such that (1+λ) isequal to a power of 2, such that the means 308 for applying thecoefficient 1/(1+λ) is a means for performing a shift of bits from theirbinary input. The means 308 can for example take the form of a shiftregister. Relative to a unit like those (reference 200 and 250)described relative to FIGS. 8A and 8B, this makes it possible to do awaywith a divider and simplify performance of the calculation.

The coefficient λ is also chosen such that λ is large before one (1<<λ).λ “large” before 1 means that λ is greater than 2¹⁰.

The coefficient λ can be configurable, possibly configurable during theidentification method.

The cost function variation J′ implemented by the unit 300 can use thefollowing relationship:J′ _(k)(n+1)=(1*j _(k)(n)+λ*J′ _(k)(n))/(1+λ)

with j_(k)(n) being the output of the means 302 forming a XOR logicgate, λ the coefficient whereof the sum with the unit corresponds to anumber N of calculation points or samples.

${J^{\prime}\left( {n + 1} \right)} = \frac{{j(n)} + {\lambda\;{j\left( {n - 1} \right)}} + {\lambda^{2}{j\left( {n - 2} \right)}} + \ldots + {\lambda^{N - 1}{j\left( {n - N + 1} \right)}}}{1 + \lambda}$

When λ is chosen such that 1<<λ, we have J′(n)≈J(n), the cost function Jbeing substantially equal to the cost function variation J′.

In FIG. 15, a structure variation 330 provided to deliver an estimationof ŷ is shown. This structure 330 differs from that previously describedrelative to FIG. 13, by the calculation of the cost function, andincludes nh units 300 ₀, . . . , 300 _(i), . . . , 300 _(nh−1) forevaluating cost function elements J′ like that (referenced 300) justdescribed relative to FIG. 14.

In FIG. 16, another example of a calculation unit 350, making itpossible to perform the calculation of an element J″_(k) of another costfunction variation J″, is given.

This unit 350 comprises a means 352 forming an exclusive OR logic gate(XOR) at the input of which an output s_(k) of the comparator 120 at amoment k is transmitted, and an input signal u_(k−i) of the system 100.

The unit 350 also comprises a means 353 a making it possible to apply aratio (1/λ), at the output pk(n) of the XOR gate, as well as a means 354forming a summer at the output of the means 353 a, a means 356 forming afirst order delay filter at the output of the summer 354 and the outputof which is reinjected at the input of a means 353 b making it possibleto apply a ratio (1/λ), the output of the means 353 b and the filter 356being transmitted to the input of the summer 354. At the output of thesummer 354, an element of said second cost function variation J″ isobtained.

The sum (1+λ) of the coefficient λ and the unit corresponds to a numberN of calculation points.

In this example, the coefficient λ is chosen equal to a power of 2:λ=2^b.

The means 353 a and 353 b are also capable of performing a shift oftheir binary input, each to apply the ratio 1/λ, which amounts toapplying a shift of b bits to the right.

In relation to the structure 300 described relative to FIG. 15, thismakes it possible to do away with multipliers.

This other variation of a calculation unit 350 is implemented with acoefficient λ chosen such that λ is large before 1(1<<λ). “Large” λmeans that λ is greater than at least 2¹⁰.

${J_{k}^{\prime}\left( {n + 1} \right)} = {\frac{{j_{k}(n)} + {\lambda\;{J_{k}(n)}}}{1 + \lambda} = {\frac{j_{k}(n)}{1 + \lambda} + \frac{\lambda\;{J_{k}(n)}}{1 + \lambda}}}$${J_{k}^{''}\left( {n + 1} \right)} = {\frac{j_{k}(n)}{1 + \lambda} + \frac{\lambda\;{J_{k}(n)}}{1 + \lambda}}$${J_{k}^{''}\left( {n + 1} \right)} = {{\frac{1}{\lambda}{j_{k}(n)}} + \frac{\;{J_{k}(n)}}{1 + {1/\lambda}}}$${J_{k}^{''}\left( {n + 1} \right)} = {{\frac{1}{\lambda}{j_{k}(n)}} + {\sum\limits_{m}^{\;}{\left( {- 1} \right)^{m}\left( \frac{1}{\lambda} \right)^{m}{J_{k}(n)}}}}$

Considering the limited second order development, we have the followingrelationship:

${J_{k}^{''}\left( {n + 1} \right)} = {{\frac{1}{\lambda}{j_{k}(n)}} + {J_{k}(n)} - {\frac{1}{\lambda}{J_{k}(n)}}}$

When λ is chosen such that 1<<λ, we have J″(n)≈J(n), the cost function Jbeing substantially equal to the cost function variation J″.

In FIG. 17, a structure variation 430 provided to deliver an estimationof ŷ is shown. This structure 430 differs from that previously describedrelative to FIG. 14, by the calculation of the cost function, andincludes nh units 350 ₀, . . . , 350 _(i), . . . , 350 _(nh−1) forevaluating the cost function J″ like that (referenced 350) justdescribed relative to FIG. 16.

Another example of a structure 530 provided to deliver an estimation ŷof the output of the system 100 is given in FIG. 18. In this example,the means for applying a passage function f from a cost function elementJi to an impulse response element ĥi differs from that of the structures230, 330 previously described relative to FIGS. 13 and 15. In thisexample, the number of LUTs is greatly reduced relative to that of thestructures 230 and 330. We go from nh LUTs, i.e. one LUT per level, to asingle LUT for the nh levels of the structure.

To that end, a first multiplexer means 362 is provided at the output ofthe nh units 350 ₀, . . . , 350 _(i), 350 _(nh−1) for calculating thecost function J″ like that (referenced 350) described relative to FIG.16.

As a function of a selection signal transmitted by a control module 365,the first multiplexor means 362 transmits, as output, an input selectedfrom a plurality of its inputs.

As output of the first multiplexer means 362 is a means 360 for examplein the form of a LUT, to apply the passage function f.

A demultiplexer means 364 is provided at the output of the LUT 360. Theinput of the second demultiplexer means 364 is transmitted towards oneof its outputs selected by a selection signal delivered by the controlmodule 365. The outputs of the demultiplexer means 364 deliver elementsĥ0, . . . ĥi, ĥnh−1, respectively, for estimating an impulse response.

The control module 365 is thus provided to transmit selection signalstowards the multiplexer means 362, and towards the demultiplexer means364, so as to ensure good routing of the estimated impulse responsevalues.

The structure 430 also includes the nh units 270 ₀, 270 ₁, . . . , 270_(i), . . . , 270 _(nh−1) to perform the convolution operation leadingto the estimation ŷ.

The operation of one or the other of the structures 230, 330, 430, 530has been presented up to now with a given number of levels nh. Thisnumber nh corresponds to a number of elements of the impulse responsethat one is seeking to identify, and can be modified or adapted.

The number of elements nh of the impulse response identified can bechosen depending on the complexity of the system 100 and the samplingfrequency fs. The number nh of elements to be identified is greater thanthe number of non-zero elements n0 of the impulse response of theobserved system: such that nh>n0. This number nh depends on features ofthe system 100, such as damping, and the sampling frequency fs. Thegreater the oversampling, the more levels nh will be provided for agiven damping. The choice of the number nh is made so as to respectShannon's theorem. In the case, for example, where the system to beidentified is an electrical oscillator, the sampling frequency fs can beprovided such that fs>2*fc with fc being the cutting frequency of theoscillator.

The number nh of levels is preferably small before λ, coefficient of thecost function calculation units. For example, λ can be considered to beat least 2⁸ times larger than nh and λ can assume values between 2¹⁰ and2²⁰.

Another example of a structure 630 provided to deliver an estimation ŷis given in FIG. 19.

In this structure 630, a parallelization of the nh levels has been done,such that the structure 630 has one level.

To that end, at the output of the delay filters 240 ₁, . . . , 240_(nh−1), a multiplexer means 545 is provided controlled by a controlsignal transmitted by a control module 565.

At the output of the multiplexing means 545, a unit 550 for calculatingthe elements of a cost function J″ is provided. This level differs fromthat (referenced 350) previously described relative to FIG. 16 in thatthe means 356 forming a delay filter with z transfer function equal toz⁻¹, is replaced by a module 556 including a means forming a memory 557,a means forming a multiplexer 558 connected to the memory, and a meansforming a demultiplexer 559 connected to the memory. The memory 557 isprovided to store values of elements J″₀, . . . j″_(i), . . . ,J″_(nh−1) of cost function J″.

In order to calculate an element J″(n+1) of the cost function, anearlier cost function element or one previously calculated J″(n) isextracted from the memory 557 and transmitted as output from themultiplexer 558 in order to be injected at the input of a summer and ameans for applying a ratio (1/λ).

The multiplexer 558 and the demultiplexer 559 are controlled by signalstransmitted by the control module 565.

Once calculated, an element of the cost function is transmitted at theinput of the demultiplexer means 559, to be placed in the memory 557.

As the output of the calculation level of J″, a LUT 560 is placedprovided to receive a cost function element J″I and produce, as output,a corresponding impulse response element ĥi.

This impulse response element ĥi may be transmitted towards amultiplexer 580 connected to a memory 582, then stored in said memory582.

A convolution calculation module 570 is also provided at the output ofthe LUT 560. This module 570 comprises a means 571 forming a multiplierfor multiplying the output of the LUT 560 delivering an impulse responseestimation element ĥ i, at the output of the multiplexer means 545delivering an input signal u of the system among the signals u_(k), . .. , u_(k−i), . . . , u_(nh−1). A means forming a summer 572 is providedto perform an addition of the output of the multiplier and a multiplexer574. The output of the summer is reinjected at the input of themultiplexer 574 after having passed through a delay filter 575. Themultiplexer 574 is also controlled by the control block 565.

At the output of the summer, an estimation ŷ is obtained.

The value of the coefficient λ can be modified, possibly during theidentification method.

The choice of a low coefficient λ, for example less than 2⁸, makes itpossible to give substantial weight to the new samples, and to obtainprocessing in which speed is favored over precision.

The choice of a high coefficient λ (with b>2¹⁵) makes it possible tofavor precision over speed.

The parameter λ can thus be made to evolve during the identificationprocessing, depending on the progress of the impulse responseestimation.

Another example of a device for implementing the identification methodaccording to the invention is given in FIG. 20.

With such a device, during the processing done, the coefficient λparticipating in the calculation of the cost function J is made toevolve.

Feedback or looping back is done at a structure 730 receiving the inputsignal u of the system and the output signal s of the comparator 120 andprovided to deliver an estimation of ŷ. The structure 730 can be one ofthose 330, 430, 530, 630 previously described, with a control block 680as output.

The control block 680 can comprise a calculation unit includingcomponents similar to those of the calculation unit described relativeto FIG. 16. The block 680 receives, as input, the output signal s of thecomparator 120 at a moment k, and the estimation ŝk coming out of thecomparator 140.

The control block 680 can comprise a means 683 forming an exclusive ORlogic gate (XOR) at the input of which the signals sk and ŝk aretransmitted.

The level 689 also comprises a means 684 making it possible to apply aratio (1/λ), for example with the aid of a shift register, at the outputof the XOR gate, as well as a means 686 forming a summer at the outputof the means 684, a means 687 forming a first order delay filter andwith transfer function z⁻¹ at the output of the summer 686 and theoutput of which is reinjected at the input of a means 685 making itpossible to apply a ratio (1/λ), for example with the aid of at leastone shift register, the output of the means 685 and the filter 687 beingtransmitted at the input of the summer 686.

Thus, the calculation level 689 performs the calculation of a secondcriterion it to estimate the error on ŝ_(k), relative to s_(k), with itsuch that:

${{Jt}(k)} \approx {\frac{1}{N}{\sum\limits_{N}^{\;}{{XOR}\left( {{s(k)},{\hat{s}(k)}} \right)}}}$(N: the number of calculation points equal to 1+λ)

The value of the coefficient λ is controlled, as a function of theobtained value of J_(t). A function f_(t) is then applied in order todetermine a control law such as:λ(k)=ƒ_(t)(Jt(k))

In the case of FIG. 16, we have λ=2^(^b). The modification of λ amountsto a modification of b, we can therefore find a function ft such as:b(k)=ƒ_(t)(Jt(k))

The function f_(t) can be applied via a LUT 688.

According to one alternative, the coefficient λ can be steered from thefunction J_(t), while being free from the use of a LUT 680.

A linear relationship can be implemented between the parameter λ andJ_(t).

FIG. 21 shows an example of a means 780 for applying a linear control,corresponding to the equation:λ=α*Jt+β where β≠0 to avoid the case λ=0.The LUT can then be replaced with this means 780, which includes amultiplier means 781 and a summer means 782.

In FIG. 22, an example of a straight line C₁₀₀ representative of alinear control of the coefficient λ is given.

FIG. 23 shows the contribution of the feedback and the control block630. In this figure, a first curve C₂₀₀ is representative of theevolution of the estimation of the impulse response done withoutfeedback. A second curve C₂₀₂ is representative of the evolution of theestimation of the impulse response done with a feedback loop providedwith the control block 680.

Another example of a device according to the invention is given in FIG.24.

This device comprises a noise generator 110, for example a pseudo-randomsignal generator of the 32nd order LFSR type, which can for exampledeliver a signal with an amplitude between 0 and 3 volts. At the outputof the generator 110, a level shifter circuit 802 is provided and candeliver a signal for example between −0.5 volts and 0.5 volts. Thedevice also comprises a first buffer circuit 810 at the input of asystem 1000 to be identified, and a second buffer circuit 820 at theoutput of the system 1000. A comparator 120 is provided at the output ofthe second buffer circuit 820 and delivers the signal s to a means 830,for example one of the structures 130, 230, 330 previously described, toestimate the output of the system 1000. The means 830 also receives anoise signal u coming from the generator. The means 830 can for examplebe implemented with the aid of a FPGA.

In this example, the system 1000 can be a resonant second order RLCfilter, whereof the transfer function H uses the following relationship:

${H(p)} = \frac{\frac{k}{R_{1}R_{3}C_{1}C_{2}}}{p^{2} + {p\left\lbrack {{\left( {1 - k} \right)\frac{1}{R_{3}C_{1}}} + \frac{1}{R_{1}C_{2}} + \frac{1}{R_{3}C_{2}}} \right\rbrack} + \frac{1}{R_{1}R_{3}C_{1}C_{2}}}$$k = {1 + \frac{R_{a}}{R_{b}}}$with:

$\varpi_{0} = \frac{1}{\sqrt{R_{1}R_{3}C_{1}C_{2}}}$$\frac{1}{Q} = {\sqrt{\frac{R_{3}C_{1}}{R_{1}C_{2}}} + \sqrt{\frac{R_{1}C_{1}}{R_{3}C_{2}}} + {\left( {1 - k} \right)\sqrt{\frac{R_{1}C_{2}}{R_{3}C_{1}}}}}$

The resonance frequency of the filter can be in the vicinity of 1500 Hz,while the sampling frequency fs chosen is 5 kHz. Such a system 1000 canhave an impulse response with the shape of curve C₃₀₀.

One example of a program implemented using the Matlab tool, to implementan impulse response estimation according to the invention, is providedin the annex. This program includes a function, having for inputs theinput signal u and the output signal s, the number of levels nh, thecoefficient value λ and the number of points nb_pts for parametercalculations. This function returns data hhat, corresponding to theestimation ĥ of the impulse response h of the observed system.

The implementation of the BIMBO_inline method can be done by amicrocomputer including a calculation section with all of the electroniccomponents, software or other, needed for the processing. Thus, forexample, the microcomputer in particular includes at least oneprogrammable processor, as well as at least one memory for thisprocessing.

The processor can, for example, be a microprocessor, a DSP, or a centralprocessing unit. The memory can for example be a hard drive, a read-onlymemory ROM, a CD-ROM, a dynamic random access memory DRAM, or any othertype of memory RAM, a magnetic or optical storage element, registers orother volatile or non-volatile memory.

A program, making it possible to implement the method according to theinvention, can be resident or recorded on a medium (e.g. floppy disk orCD ROM or DVD ROM or removable hard drive or magnetic medium) that canbe read by a computer system or by the microcomputer.

According to one possibility, the BIMBO_inline algorithm and the noisegenerator can be implemented with the aid of a FPGA, the other elements,in particular the one-bit ADC, being able to take the form of discretecomponents.

The identification method can be used in the context of BIST (Built InSelf Test) systems, i.e. systems with the ability to test themselves.This makes it possible to avoid the use of significant equipment duringa test. In this case this involves applying the presented BIMBO_inlinemethod to a system and comparing the desired and actual impulseresponses to conclude on proper operation of the system.

The identification method can be used to perform auto-calibration of asystem, in particular an electromechanical system. During its operation.Such a system can be considered to evolve over time. The methodaccording to the invention then makes it possible to estimate theseevolutions, with the aid of estimations of the impulse response of thesystem, and to adapt the control system as a function thereof.

The estimation of the impulse response can be completed by a transferfunction identification.

The method according to the invention has been tested on a universalactive filter UAF42 by the company Texas Instrument and as shown in FIG.28, with a sampling frequency for example in the vicinity of 15 kHz, andresistance values RF1=RF2=220 kΩ, RG=22 kΩ, RQ=10 kΩ. Such valuescorrespond to a quality factor Q=1.2, and a natural frequency fo in thevicinity of 730 Hz.

FIGS. 28 and 29 give amplitude C400 and gain C500 estimation curves ofthe filter obtained with 100 impulse response coefficients after 4000samples at the output of a device, for example as described relative toFIG. 13, have been obtained.

By way of comparison, experimental amplitude C₄₀₂ and gain C₅₀₂ curvesare provided.

In FIG. 30, another example of a device according to the invention isprovided. This device is provided with a means 830, for example one ofthe structures 130, 230, 330 previously described, for implementing theBIMBO_inline method and performing an estimation ŷ_(k) of the output ofa system 1000, which delivers a signal s_(k). The means 830 alsoreceives a noise signal u from the generator.

The presented BIMBO_inline algorithm receives the signals u and s fromthe noise generator and the comparator, respectively (analog digitalconverter), and provides an estimation ŷ_(k) of the signal y_(k) fromthe estimation of the impulse response. This estimation of the output ofthe observed system is used by a parametric adaptation algorithm.

The means 900 and 810 produce a parametric adaptation algorithm and usethe output y_(k) of the system. We therefore consider that ŷ_(k)=y_(k).

The block 810 contains the approximate model of the observed system.This approximate model is an IIR type model (modeling in the form of anumerator/denominator transfer function with Infinite Impulse Response).This model is reevaluated at each sampling period by the block 900,which comprises the parametric adaptation algorithm therein, for examplethe algorithm of least squares. At each sampling period, the approximatemodel provides an estimation {circumflex over (ŷ)}_(k) of ŷ_(k). Theparametric adaptation algorithm will provide a new estimation of theapproximate model, including the output, by minimizing the error between{circumflex over (ŷ)}_(k) and ŷ_(k).

ANNEX function [hhat] = verif_bimbo_inline(u,s,nh,nb_pts,a,b) %initialization u_delay_line=zeros(nh,1); Csu=0.5*ones(nh,1); %processing loop for k=1:nb_pts u_delay_line=[u(k);u_delay_line(1:end−1)]; J=a/b*xor(s(k),u_delay_line)+J−a/b*J; %estimation of hhhat=sqrt(2)*erfinv(−2*J+1)./sqrt(1+2*erfinv(−2*J+1).{circumflex over( )}2); % estimation of y ( reframing of u (0,1)=>(1,−1) ) yhat=(−2*u_delay_line+1)*hhat; end;

The invention claimed is:
 1. A device for identifying an electronic orelectromechanical system, comprising: a noise generator for generating anoise signal (u_(k)), intended to generate the noise signal at the inputof said system; a one-bit analog digital converter, to which an outputsignal (s_(k)) of the system is intended to be applied; an estimationdevice for carrying out an estimation (ĥ) of the impulse response ofsaid system comprising: first calculation means to perform an iterativecalculation of a plurality of nh (with nh being an integer) elements(J₀, . . . , J_(i, . . . ,) J_(nh−1)) of a given criterion J, eachelement including at least one correlation term between said signaloutput from said converter and said noise signal; means for making anestimation (ĥ_(k)) of the output of said system with the aid of saidestimation of the impulse response of said system, said means comprisinga second calculation means to apply, to the calculated elements (J₀, . .. , J_(i, . . . ,) J_(nh−1)) of said given criterion J, a passagefunction f predetermined as a function of the noise signal (u_(k))transmitted at the input of said system, and such that:${f(J)} = {\sum\limits_{i = 0}^{{nh} - 1}\;{h_{i}{\hat{h}}_{i}}}$ withh_(i) an impulse response element h of said system and ĥ_(i) an elementof said impulse response estimation ĥ of said system, wherein thepassage function f is a function chosen so that each element Ji of thegiven criterion J and each element of said impulse response estimationof said system satisfy the relationship ĥ_(i)=(f(J_(i))), with${J_{i} = {{\frac{1}{2} - {\frac{1}{2\; N}{\sum\limits_{N}{{s(k)}{u\left( {k - i} \right)}\mspace{14mu}{or}\mspace{14mu} J_{i}}}}} = {\frac{1}{\; N}{\sum\limits_{N}{{XOR}\left( {s_{k},u_{k - i}} \right)}}}}},$ N being a number of samples, k being a moment, s being the outputsignal, and u being the noise signal.
 2. The device according to claim1, wherein said input signal (u_(k)) of the system is a binary whitenoise signal, said passage function f following the relationship:${f(J)} = {\sigma\sqrt{2}{\frac{{erf}^{- 1}\left( {1 - {2J}} \right)}{\sqrt{1 + {2\left( {{erf}^{- 1}\left( {1 - {2J}} \right)} \right)^{2}}}}.}}$3. The device according to claim 1, wherein the estimation devicecomprises: a chain of blocks respectively forming a first order delayfunction or having z⁻¹ as z transfer function, said chain being intendedto receive said input signal (u_(k)), and to transmit values (u_(k), . .. u_(k−i), u_(k−nh−1)) of the delayed noise signal at the output of saidblocks, respectively.
 4. The device according to claim 1, wherein saidfirst calculation means comprises: means forming an exclusive OR logicgate, to perform an exclusive OR logic operation between said outputsignal (s_(k)) of said converter taken at a moment k and said noisesignal (u_(k−i), with 0≦i≦nh) delayed by i relative to said givenmoment, adding means, to add the result of said logic operation to aterm depending on an element of said given criterion calculatedpreviously.
 5. The device according to claim 1, wherein the acquisitionof said output signal (S_(k)) at the output of said converter is donefor a given number (N) of samples, the calculation of the givencriterion J by the first calculation means being dependent on at leastone predetermined coefficient λ, λ being equal to said given number (N)of samples.
 6. The device according to claim 5, further comprising meansfor modifying the coefficient value λ during said estimation (ĥ) of saidimpulse response.
 7. The device according to claim 5, the firstcalculating means comprising means making it possible to apply saidcoefficient λ in the form of at least one shift register and/or meansfor applying a ratio 1/(1+λ) in the form of at least one shift register.8. The device according to claim 7, the first calculating meanscomprising means making it possible to apply a ratio (1/λ) in the formof at least one shift register.
 9. The device according to claim 6,wherein said modification of the coefficient λ can be done as a functionof the evaluation of a second criterion Jt, the device furthercomprising: means for evaluating said second criterion Jt including atleast one exclusive OR logic gate (XOR) to perform an exclusive OR logicoperation (XOR) between said output signal (S_(k)) from said converterand an estimation (Ŝ_(k)) of that signal, adding means, for adding theresult of said logic operation between said output signal (s_(k)) fromsaid converter and an estimation (Ŝ_(k)) of that signal, to a termdepending on an element of said second criterion previously calculated.10. The device according to claim 9, the modification of the coefficientλ being done as a function of the evaluation of said second criterionJt, according to the following relationship:λ=α*Jt+β(with α>0 and β>0).
 11. The device according to claim 1, saidmeans for performing said estimation (ĥ_(k)) comprising a means forconvolution calculation between the estimated impulse response (ĥ) andthe noise input signal (u_(k)).
 12. The device according to claim 1,said system being an electronic filter or a MEMS.
 13. A method ofidentifying an electronic or electromechanical system comprising:applying at least one noise signal (u_(k)) as input to the system;applying an output signal (s_(k)) of said system to a one-bit analoguedigital converter; carrying out an estimation of the output of saidsystem with the aid of means for performing an estimation (ĥ) of theimpulse response of said system, the estimation (ĥ) of said impulseresponse comprising: the iterative calculation of a plurality of nh (nhbeing an integer) elements (J₀, . . . , J_(i, . . . ,) J_(nh−1)) of agiven criterion J, each element including at least one term ofcorrelation between said signal at the output of said converter and saidnoise signal, estimating the output of said system with the aid of saidestimation of the impulse response of said system, said estimatingcomprising the application to said calculated elements (Ji) of the givencriterion (J) of a passage function (f), said passage function (f) beingpredetermined as a function of said signal applied at the input of saidsystem, and such that:${f(J)} = {\sum\limits_{i = 0}^{{nh} - 1}{h_{i}{\hat{h}}_{i}}}$  withh_(i), an impulse response element h of said system and ĥ_(i) an elementof said impulse response estimation ĥ of said system among a pluralityof nh impulse response elements (ĥ₀, . . . , ĥ_(i, . . . ,) ĥ_(nh−1)),wherein the passage function f is a function chosen so that each elementJi of the given criterion J and each element of said impulse responseestimation of said system satisfy the relationship ĥ_(i)=(f(J_(i))),with${J_{i} = {{\frac{1}{2} - {\frac{1}{2\; N}{\sum\limits_{N}{{s(k)}{u\left( {k - i} \right)}\mspace{14mu}{or}\mspace{14mu} J_{i}}}}} = {\frac{1}{N}{\sum\limits_{N}{{XOR}\left( {s_{k},u_{k - i}} \right)}}}}},$ N being a number of samples, k being a moment, s being the outputsignal, and u being the noise signal.
 14. The method according to claim13, wherein said input signal (u_(k)) of the system is a binary whitenoise signal, said passage function f following the relationship:${f(J)} = {\sigma\sqrt{2}{\frac{{erf}^{- 1}\left( {1 - {2J}} \right)}{\sqrt{1 + {2\left( {{erf}^{- 1}\left( {1 - {2J}} \right)} \right)^{2}}}}.}}$15. A device for identifying an electronic or electromechanical system,comprising: a noise generator for generating a noise signal (u_(k)),intended to generate a noise signal at the input of said system; aone-bit analog digital converter, to which an output signal (s_(k)) ofthe system is intended to be applied; an estimation device for carryingout an estimation (ĥ) of the impulse response of said system comprising:first calculation means to perform an iterative calculation of aplurality of nh (with nh being an integer) elements (J₀, . . . ,J_(i, . . . ,) J_(nh−1)) of a given criterion J, each element includingat least one correlation term between said signal output from saidconverter and said noise signal; means for making an estimation (ĥ_(k))of the output of said system with the aid of said estimation of theimpulse response of said system, said means comprising a secondcalculation means to apply, to the calculated elements (J₀, . . . ,J_(i, . . . ,) J_(nh−1)) of said given criterion J, a passage function fpredetermined as a function of the noise signal (u_(k)) transmitted atthe input of said system, and such that:${f(J)} = {\sum\limits_{i = 0}^{{nh} - 1}{h_{i}{\hat{h}}_{i}}}$ withh_(i) an impulse response element h of said system and ĥ_(i) an elementof said impulse response estimation ĥ of said system, wherein said inputsignal (u_(k)) of the system is a binary white noise signal, saidpassage function f following the relationship:${f(J)} = {\sigma\sqrt{2}{\frac{{erf}^{- 1}\left( {1 - {2J}} \right)}{\sqrt{1 + {2\left( {{erf}^{- 1}\left( {1 - {2J}} \right)} \right)^{2}}}}.}}$16. A device for identifying an electronic or electromechanical system,comprising: a noise generator for generating a noise signal (u_(k)),intended to generate a noise signal at the input of said system; aone-bit analog digital converter, to which an output signal (s_(k)) ofthe system is intended to be applied; an estimation device for carryingout an estimation (ĥ) of the impulse response of said system comprising:first calculation means to perform an iterative calculation of aplurality of nh (with nh being an integer) elements (J₀, . . . ,J_(i, . . . ,) J_(nh−1)) of a given criterion J, each element includingat least one correlation term between said signal output from saidconverter and said noise signal; means for making an estimation (ĥ_(k))of the output of said system with the aid of said estimation of theimpulse response of said system, said means comprising a secondcalculation means to apply, to the calculated elements (J₀, . . . ,J_(i, . . . ,) J_(nh−1)) of said given criterion J, a passage function fpredetermined as a function of the noise signal (u_(k)) transmitted atthe input of said system, and such that:${f(J)} = {\sum\limits_{i = 0}^{{nh} - 1}{h_{i}{\hat{h}}_{i}}}$ withh_(i) an impulse response element h of said system and ĥ_(i) an elementof said impulse response estimation ĥ of said system, wherein said firstcalculation means comprises: means forming an exclusive OR logic gate,to perform an exclusive OR logic operation between said output signal(s_(k)) of said converter taken at a moment k and said noise signal(u_(k−i), with 0≦i≦nh) delayed by i relative to said given moment,adding means, to add the result of said logic operation to a termdepending on an element of said given criterion calculated previously.